Worth beginning with dx9?

Tutorials can be hard to find for DX10 and DX11, but I guess it would just depend on what your target machines are.
If your looking to develop a game that is still going to work on windows XP go with dx9, if not I have heard that DX10 is significantly better to work with.

I wouldn't bother learning DX9 it's pretty depreciated now. I'd go for DX11 as it's basically DX10 with a few different features.

Either go for DX9 or DX11, don't bother with DX10. DX11 will run on all hardware that DX9 runs on, there are just a few (advanced) features that is only available on DX11 level hardware. DX11 is much nicer to work with, since Microsoft really cleaned up the interface and removed many of the strange idiosyncrasies from the API. Also, the fact that all the fixed function stuff have been pulled out means that you wont accidentally learn bad habits.

Don't be tempted to think that DX9 is "easier" than DX11 because of the lower version number, both are going to require some effort to learn. Here DX9 have an edge because there are a lot more tutorials aimed at DX9.

Depends entirely on your target audience as has been said. There are still lots of XP boxes and older graphics cards in use, but probably not among what the popular press insists on calling "hard-core gamers".

Crysis 4? Probably safe to leverage the additional power of DX11. Sims 36? Not safe, you would be crippling your sales based on the likely hardware of your demographic.

But, as I understand things, you don't actually get any more power from using 10 or 11 as such - a more-modern card that supports them will also render triangles quicker using DX9. It's more the flexibility you get from the more complex shader systems as far as I can tell. Do you need this flexibility?

If you want to support Windows XP, use DX9. If not, use DX11. That's all there is to it really.

Try opengl it's a very... procedural api for creating graphics.

A lot of people still use XP, which only goes up to 9. If you don't care about inclusion, then no. If you want to make it run on XP, then yes.

A lot of people still use XP, which only goes up to 9. If you don't care about inclusion, then no. If you want to make it run on XP, then yes.

Most people use windows 7. Check this out.
So I would go with directX 11

It depends on who exactly you are marketing this game engine to. Novices or experts? Are you going to release the source code so that it can be modified by a paying third party? Is this total general purpose or another FPS engine? Where do your priorities lay?

It would be wise to make the choice of DirectX9, DirectX10 or DirectX11 not by which one has the prettiest graphics but by what satisfies the needs of your clients. Its very expensive to have bleeding edge graphics, good documentation, and a good support team/community all at the same time.

A lot and most are not the same thing. As you can see, 7 and XP are about tied anyway (I see Vista also has a good share, what's up with that?). Besides, that just shows what OS's are most used, nothing about demographics of the users.